2010/10/06 by Claire Amiot, Amiot, Claire, Steffen Oppermann +1
Mathematics · Physics and Astronomy · #16E #16G #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1010.1129
openalex publication_date 2010/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cluster categories of hereditary algebras have been introduced as orbit categories of their derived categories. Keller has pointed out that for non-hereditary algebras orbit categories need not be triangulated, and he introduced the notion of triangulated hull to overcome this problem. In this paper we study the image if the natural functor from the bounded derived category to the cluster category, that is we investigate how far the orbit category is from being the cluster category. We show that for wide classes of non-piecewise hereditary algebras the orbit category is never equal to the cluster category.